A Relatively Simple Form of the Distribution of the Multiple Correlation Coefficient

Abstract

A series is obtained for the cumulative distribution function of the multiple correlation coefficient in which the coefficients are interpretable as binomial probabilities. WhenN—pis even (Nis the sample size andpis the number of components in the underlying multivariate normal distribution) the series is finite with 1/2(n – p) + 1 terms. Other series are also considered. A comparatively simple approximation to the general distribution of the multiple correlation coefficient is presented which, in particular forp= 2, is more accurate than Fisher's z-transform over a large set of values of the parameters involved.